【摘要】：隨著信息化社會(huì)的飛速發(fā)展,統(tǒng)計(jì)已經(jīng)滲透到社會(huì)生活的各個(gè)領(lǐng)域。近年來,國內(nèi)重視統(tǒng)計(jì)教育的呼聲越來越高。不過,相對(duì)于國外比較成熟的統(tǒng)計(jì)教育研究,國內(nèi)相關(guān)研究才剛剛起步,還需要相關(guān)研究人員開展大量的理論性研究。本研究的主要目的是希望通過調(diào)查數(shù)學(xué)系大一學(xué)生對(duì)于標(biāo)準(zhǔn)差概念理解的現(xiàn)狀來呼吁教師重視標(biāo)準(zhǔn)差的概念教學(xué)。同時(shí),對(duì)于學(xué)生理解標(biāo)準(zhǔn)差概念的困難有所發(fā)現(xiàn),為改進(jìn)教學(xué)提供一些理論研究的依據(jù)。 本研究主要采用定性與定量的研究方法,通過問卷調(diào)查和訪談收集數(shù)據(jù),使用獨(dú)立樣本t檢驗(yàn)和方差分析的數(shù)據(jù)分析方法。本研究主要通過以下四個(gè)方面探究數(shù)學(xué)系大一學(xué)生對(duì)于標(biāo)準(zhǔn)差的概念性理解：(1)學(xué)生對(duì)于標(biāo)準(zhǔn)差的數(shù)學(xué)內(nèi)涵和統(tǒng)計(jì)意義的理解如何；(2)學(xué)生是否會(huì)判斷不同呈現(xiàn)方式下的數(shù)據(jù)的標(biāo)準(zhǔn)差大小以及判斷的策略有哪些；(3)學(xué)生利用標(biāo)準(zhǔn)差進(jìn)行決策的水平如何；(4)學(xué)生對(duì)于標(biāo)準(zhǔn)差概念的理解水平是否存在明顯的性別差異,專業(yè)差異以及生源地差異。 研究結(jié)果發(fā)現(xiàn)：(1)數(shù)學(xué)系大一學(xué)生對(duì)于標(biāo)準(zhǔn)差的數(shù)學(xué)內(nèi)涵和統(tǒng)計(jì)意義綜合掌握情況較好,但學(xué)生對(duì)于標(biāo)準(zhǔn)差公式內(nèi)涵的理解不透徹,正確描述標(biāo)準(zhǔn)差公式的人數(shù)偏少。(2)學(xué)生對(duì)于標(biāo)準(zhǔn)差的概念性理解偏弱,綜合考慮影響標(biāo)準(zhǔn)差大小的各種因素的能力欠佳。表現(xiàn)為判斷標(biāo)準(zhǔn)差大小的有效策略偏少；學(xué)生比較標(biāo)準(zhǔn)差大小時(shí)受到數(shù)據(jù)不同呈現(xiàn)方式的影響,他們?cè)谂袛鄡煞陨现狈綀D的標(biāo)準(zhǔn)差大小時(shí)表現(xiàn)最差。(3)大部分學(xué)生在根據(jù)抽樣信息決策時(shí),會(huì)考慮使用標(biāo)準(zhǔn)差,并且能夠正確使用標(biāo)準(zhǔn)差幫助決策。(4)學(xué)生對(duì)于標(biāo)準(zhǔn)差概念的理解水平?jīng)]有表現(xiàn)出明顯的性別差異,但存在顯著的專業(yè)差異和生源地差異。具體為師范專業(yè)的學(xué)生對(duì)于標(biāo)準(zhǔn)差概念的理解水平明顯低于非師范專業(yè)的學(xué)生,西部地區(qū)的學(xué)生的表現(xiàn)也明顯弱于中部、東部地區(qū)的學(xué)生。 最后,基于本研究的發(fā)現(xiàn),本文對(duì)于標(biāo)準(zhǔn)差的概念教學(xué)提出了建議。
[Abstract]:With the rapid development of information society, statistics has penetrated into all fields of social life. In recent years, the domestic attention to statistical education is getting louder and higher. However, relative to the more mature statistical education research abroad, the domestic research has just started, and a large number of theoretical research is needed. The main purpose of this study is to appeal to teachers to pay more attention to the concept teaching of standard deviation by investigating the present situation of students' understanding of standard deviation. At the same time, the difficulty of students understanding the concept of standard deviation is found, which provides some theoretical basis for improving teaching. This study mainly adopts the qualitative and quantitative research methods, collects the data through the questionnaire survey and the interview, uses the independent sample t-test and the analysis of variance data analysis method. This research mainly through the following four aspects to explore the mathematical freshmen's conceptual understanding of the standard deviation: (1) how students understand the mathematical meaning and statistical significance of the standard deviation; (2) whether the students will judge the magnitude of the standard deviation of the data under different presentation modes and what the judgment strategies are; (3) how well the students can make decisions by using the standard deviation; (4) whether there are significant gender differences, major differences and student origin differences in students' understanding of standard deviation concepts. The results are as follows: (1) the mathematics connotation and statistical meaning of the standard deviation are well grasped by the freshmen, but the students do not have a thorough understanding of the connotation of the standard deviation formula. The number of people who correctly describe the standard deviation formula is small. (2) the students' conceptual understanding of standard deviation is weak, and the ability of synthetically considering various factors affecting the standard deviation is poor. The effective strategy of judging the magnitude of standard deviation is less; Students are affected by different presentation modes of data when comparing standard deviation. They perform the worst when judging the standard deviation of more than two histograms. (3) most students consider using standard deviation when making decisions based on sampling information. And the correct use of standard deviation to help decision-making. (4) the level of understanding of standard deviation does not show significant gender differences, but there are significant differences in professional and student origin. In particular, the level of understanding of the concept of standard deviation of the students majoring in teacher training is obviously lower than that of the students of non-normal majors, and the performance of students in the western region is obviously weaker than that in the central and eastern regions. Finally, based on the findings of this study, this paper puts forward some suggestions for the concept teaching of standard deviation.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：O212.1-4;G645.5

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本文編號(hào)：2339042